Let a function $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as:

$f(x) = \begin{cases} x + 2, & \text{if } x \leq a \\ x^2+ 5x + 6, & \text{if } x > a. \end{cases}$

Find the value of $a$ such that $f$ is continuous for all real values of $x$.

This problem is part of the set - Piecewise-defined Functions

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